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Properly integral polynomials over the ring of integer-valued polynomials on a matrix ring
Get PDFAbstractLet D be a domain with fraction field K, and let Mn(D) be the ring of n×n matrices with entries in D. The ring of integer-valued polynomials on the matrix ring Mn(D), denoted IntK(Mn(D)), consists of those polynomials in K[x] that map matrices in Mn(D) back to Mn(D) under evaluation. It has been known for some time that IntQ(Mn(Z)) is not integrally closed. However, it was only recently that an example of a polynomial in the integral closure of IntQ(Mn(Z)) but not in the ring itself appeared in the literature, and the published example is specific to the case n=2. In this paper, we give a construction that produces polynomials that are integral over IntK(Mn(D)) but are not in the ring itself, where D is a Dedekind domain with finite residue fields and n≥2 is arbitrary. We also show how our general example is related to P-sequences for IntK(Mn(D)) and its integral closure in the case where D is a discrete valuation ring
Non-triviality conditions for integer-valued polynomial rings on algebras
Get PDFLet be a commutative domain with field of fractions and let be a torsion-free -algebra such that . The ring of integer-valued polynomials on with coefficients in is \Int_K(A) = \{f \in K[X] \mid f(A) \subseteq A\}, which generalizes the classic ring \Int(D) = \{f \in K[X] \mid f(D) \subseteq D\} of integer-valued polynomials on .
The condition implies that D[X] \subseteq \Int_K(A) \subseteq \Int(D), and we say that \Int_K(A) is nontrivial if \Int_K(A) \ne D[X]. For any integral domain , we prove that if is finitely generated as a -module, then \Int_K(A) is nontrivial if and only if \Int(D) is nontrivial. When is not necessarily finitely generated but is Dedekind, we provide necessary and sufficient conditions for \Int_K(A) to be nontrivial. These conditions also allow us to prove that, for Dedekind, the domain \Int_K(A) has Krull dimension 2
Decomposition of Integer-valued Polynomial Algebras
Get PDFLet be a commutative domain with field of fractions , let be a torsion-free -algebra, and let be the extension of to a -algebra. The set of integer-valued polynomials on is , and the intersection of with is , which is a commutative subring of . The set may or may not be a ring, but it always has the structure of a left -module.
A -algebra which is free as a -module and of finite rank is called -decomposable if a -module basis for is also an -module basis for ; in other words, if can be generated by and . A classification of such algebras has been given when is a Dedekind domain with finite residue rings. In the present article, we modify the definition of -decomposable so that it can be applied to -algebras that are not necessarily free by defining to be -decomposable when is isomorphic to . We then provide multiple characterizations of such algebras in the case where is a discrete valuation ring or a Dedekind domain with finite residue rings. In particular, if is the ring of integers of a number field , we show that an -decomposable algebra must be a maximal -order in a separable -algebra , whose simple components have as center the same finite unramified Galois extension of and are unramified at each finite place of . Finally, when both and are rings of integers in number fields, we prove that -decomposable algebras correspond to unramified Galois extensions of $K
Integral Closure of Rings of Integer-Valued Polynomials on Algebras
Get PDFLet be an integrally closed domain with quotient field . Let be a torsion-free -algebra that is finitely generated as a -module. For every in we consider its minimal polynomial , i.e. the monic polynomial of least degree such that . The ring \Int_K(A) consists of polynomials in that send elements of back to under evaluation.
If has finite residue rings, we show that the integral closure of \Int_K(A) is the ring of polynomials in which map the roots in an algebraic closure of of all the , , into elements that are integral over . The result is obtained by identifying with a -subalgebra of the matrix algebra for some and then considering polynomials which map a matrix to a matrix integral over . We also obtain information about polynomially dense subsets of these rings of polynomials
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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